Snap off the stems of the artichokes, which should break cleanly, taking all their fibre with them (unless extremely young) – a test of their freshness. Wash the artichokes by plunging them up and down head first in a bowl of cold water. This will wash out any tiny snails or other undesirables which may have crept down between the leaves. Drain. Bring 3 litres (5¼ pints) of water to the boil with a small handful of coarse salt and when it boils plunge in the artichokes. Do not cover, and cook over a fierce heat for about 20 minutes. Then pull out one of the centre leaves; if its edible base is cooked but still a little crisp, the artichokes are ready. (If you find it difficult to remove a leaf, allow to cook for a little longer and try again.) When they are cooked plunge the artichokes into cold water for 4–5 minutes and then drain them. Remove the leaves, discarding all but the best, which you can keep to nibble as you cook. Remove the chokes, cut the hearts into eight pieces, as if you were cutting a tart and set them aside on a plate.
Your fishmonger will have filleted and skinned your sole (if not, the method is much the same as that for filleting John Dory). Spread out the fillets and cut them across the grain diagonally, starting at the tail end, into ribbons about the width of your little finger. Put them into a deep dish, cover with milk and leave to rest.
Peel the potato and dry it in a cloth. Slice as if you were making thin chips, 7 mm (¼ inch) thick and 4–5 cm (2 inches) long. Rinse in water (but do not soak or they will be leathery) and dry them on a cloth.
Put 1½ tablespoons olive oil and 20 g (¾ oz) butter in each of two heavy frying-pans. Half-fill a soup plate with flour; take out the fillets of sole (2) and shake them dry, then plunge them in the flour and stir them around thoroughly so that each fillet is covered with flour. Then, taking one fillet at a time, and using the flat of your hand, roll them on a wooden board so that they look like nicely-rounded goujonettes.
Heat both frying-pans and wait for the moment when the oil/ butter mixture has ceased to hiss, which tells you that it has reached the right temperature. Put the potato chips in one pan and the sole goujonettes in the other, stirring both alternately with a wooden spatula. Let the goujonettes cook for 5 minutes, and then drain them in a colander. Discard the cooking oil. The potatoes will be cooked in 10 minutes. Drain them in the same colander as the sole. This operation can be carried out an hour or more before the dish is to be finished and served, leaving you free to have a drink or to enjoy the first course of the meal.
Finishing the dish
Heat 30 g (1 oz) butter in a clean frying-pan until it rises into a pale golden foam and then clears. Put the goujonettes and the potatoes in the pan, and then add the pieces of artichoke (1). Season with salt and pepper – none should have been added before this moment. Let everything sizzle in the pan for 3 minutes, stirring carefully with a wooden spatula to avoid breaking the pieces of sole. Sprinkle with the juice of a lemon, add the chopped parsley and serve – fast.